On the use of Winters’ formula in chronic metabolic acidosis

Dear Sir,

We have read with great interest the letter published in this Journal by Rubio et al.,¹ and we would like to expound briefly our ideas on his comments.

Upon observing the value of HCO₃, Rubio et al., calculated the expected value of pCO₂ by using the famous Winters’ formula,² which consists of a linear regression with a slope of 1.5 and an interception of 8.3. Although still widely used, the Winters’ formula was proposed in the sixties. There is a more recent formula, which is a contribution made by Bushinsky et al.,³ who argued that the decrease in pCO₂ should be predicted by multiplying the decrease in HCO₃ by the factor 1.2. The relationship between pCO₂ and HCO₃ proposed by Bushinsky et al., may be found in many current textbooks; see, for example, Du Bose.^4,5

Nevertheless, these two formulas are not necessarily in conflict. In order to prove this, let us consider the normal values of HCO₃, pCO₂, namely 24 mEq/L, 40 mmHg, respectively. By introducing these numbers into the formula of Bushinsky et al., the formula reduces to the equation pCO₂ = 1.2^* HCO₃ + 11.2, that is to say, a linear regression with a slope of 1.2, an intersection of 11.2, which is not that different from Winters’ regression.

Moreover, the Winters’ formula was derived from a population where the value of HCO₃ was close to 9.9 mEq/L, while Bushinsky et al., analysed a wider range of HCO₃ values. Thanks to a more detailed statistical analysis, Bushinsky et al.³ show that, by restricting the range of HCO₃ values to a maximum of 10 mEq/L, the slope of the linear regression acquires a value of 1.5 (exactly the same slope reported by Winters), while the slope reaches 1.2 for values of HCO₃ between 10.1 and 25 mEq/L.

To summarise, in our opinion, the more accurate way to predict the expected value of pCO₂ in chronic metabolic acidosis, and hence to correctly deduce the presence of mixed acid-base disorders, is by using different formulae according to the range of HCO₃ values. Therefore, if the value of HCO₃ is greater than 10 mEq/L, as it usually happens, Bushinsky's formula should be considered. The use of Winters’ formula seems appropriate only for lower values of HCO₃.

For these reasons, in the cases reported by Rubio et al., where the value of HCO₃ is much greater than 10 mEq/L, although the use of Winters’ formula leads to the correct diagnosis (i.e., mixed acidosis), we conclude that a more orthodox approach would be to resort to the formulae of Bushinsky et al.